I'm pretty sure it's "jus," that is the broth (だし汁) made from the bones and carcasses of the duck.

鴨と筍は相性のいい組み合わせだが、パスタにしっからなじむように、鴨のジューを用い、筍は姫皮の香りと食感を出すために、繊維に添うようにかつら剥きにしている。
Duck and bamboo complement each other well, but make use of the duck jus to ensure that they blend thoroughly with the pasta, and cut lengthways around the bamboo shoots in the direction of the fibers to bring out their ** fragrance and texture.
** - sorry (not sure exactly what a "princess skin" could be!)

Recipe for Roast Duck from Chef Mark Dommen of One Market San ...
*Debone the ducks, removing the breasts and legs from the carcasses, and use the carcasses for the duck jus. You can also or ask your butcher to do this for ...
www.starchefs.com/thanksgiving/2005/html/duck_m_dommen.shtm... - 31k - Cached

Recipe for Coriander-Rubbed Duck and Foie Gras from Chef Dante ...
Place a quenelle of the honeydew melon compote next to the duck breast. Place the foie gras on top of the duck breast. Spoon the duck jus on top and around. ...
www.starchefs.com/features/melon/html/duck_foie_gras_d_bocc... - 28k -

Montparnasse Dinner Menu - New York City
Butternut Squash Risotto with Duck Confit, Porcini Mushrooms & Duck Jus. OR. “Coq au Vin” Red Wine Braised Chicken Casserole with Pearl Onions, ...
www.usmenuguide.com/montparnassedinnermenu.html - 13k - Cached -

Definitions of "jus" on the web:
# Juices of meat, fish or vegetables, reduced to sauce consistency and concentrated.
www.saffronrestauranttruro.co.uk/chef'_dictionary.htm

# [ZHOO] The French word for "juice," which can refer to both fruit and vegetable juices, as well as the natural juices exuded from meat. Jus de citron is "orange juice," while jus de viande means "juices from meat." A dish (usually meat) that is served au jus is presented with its own natural juices.
www.mychefcoat.com/terms-j.html

# JOO. Made from the pan juices of roasted foods. Juices are mixed with water, stock and wine and reduced to make a sauce. Between a stock and a glaze in flavour and richness.
www.certo.com.au/MenuSpeak.html

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Note added at 37 mins (2006-08-23 13:09:01 GMT)
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Here is a description of 姫皮:
たけのこは部分により硬さが違います。用途による使い分けをおすすめします。
* 先端のやわらかい部分（**姫皮**といいます）は酢の物やあえ物に、穂先は椀種や炊き込み御飯などにするとおいしいです。
So I guess you could say "bamboo shoot tips," although I kinda like the princessy name.....

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Note added at 44 mins (2006-08-23 13:16:08 GMT)
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度々すみません。
For かつら剥き、 I said "cut lengthways around the bamboo shoots," but that may not be clear enough(?) It's that thing (the 'true' mark of a good housewife ;-) ) that's often done with daikon on cooking shows, etc. ... effectively slicing very thinly around and around (but lengthways) in as long and continuous a piece as possible. This can then be sliced into thin strips (細切り) or the 'angel-hair' type daikon accompaniment to sashimi (つま）.....if that makes any sense.